doc-src/Intro/intro.tex
 author lcp Wed Nov 10 05:06:55 1993 +0100 (1993-11-10) changeset 105 216d6ed87399 child 184 236b655114a1 permissions -rw-r--r--
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     7

     8 \title{Introduction to Isabelle}

     9 \author{{\em Lawrence C. Paulson}\\

    10         Computer Laboratory \\ University of Cambridge \\[2ex]

    11         {\small{\em Electronic mail\/}: {\tt lcp@cl.cam.ac.uk}}

    12 }

    13 \date{}

    14 \makeindex

    15

    16 \underscoreoff

    17

    18 \setcounter{secnumdepth}{2} \setcounter{tocdepth}{2}

    19

    20 \sloppy

    21 \binperiod     %%%treat . like a binary operator

    22

    23 \newcommand\qeq{\stackrel{?}{\equiv}}  %for disagreement pairs in unification

    24 \newcommand{\nand}{\mathbin{\lnot\&}}

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    26

    27 \pagenumbering{roman}

    28 \begin{document}

    29 \pagestyle{empty}

    30 \begin{titlepage}

    31 \maketitle

    32 \thispagestyle{empty}

    33 \vfill

    34 {\small Copyright \copyright{} \number\year{} by Lawrence C. Paulson}

    35 \end{titlepage}

    36

    37 \pagestyle{headings}

    38 \part*{Preface}

    39 \index{Isabelle!overview}

    40 \index{Isabelle!object-logics supported}

    41 Isabelle~\cite{paulson86,paulson89,paulson700} is a generic theorem prover.

    42 It has been instantiated to support reasoning in several object-logics:

    43 \begin{itemize}

    44 \item first-order logic, constructive and classical versions

    45 \item higher-order logic, similar to that of Gordon's {\sc

    46 hol}~\cite{gordon88a}

    47 \item Zermelo-Fraenkel set theory~\cite{suppes72}

    48 \item an extensional version of Martin-L\"of's Type Theory~\cite{nordstrom90}

    49 \item the classical first-order sequent calculus, {\sc lk}

    50 \item the modal logics $T$, $S4$, and $S43$

    51 \item the Logic for Computable Functions~\cite{paulson87}

    52 \end{itemize}

    53 A logic's syntax and inference rules are specified declaratively; this

    54 allows single-step proof construction.  Isabelle provides control

    55 structures for expressing search procedures.  Isabelle also provides

    56 several generic tools, such as simplifiers and classical theorem provers,

    57 which can be applied to object-logics.

    58

    59 \index{ML}

    60 Isabelle is a large system, but beginners can get by with a small

    61 repertoire of commands and a basic knowledge of how Isabelle works.  Some

    62 knowledge of Standard~\ML{} is essential, because \ML{} is Isabelle's user

    63 interface.  Advanced Isabelle theorem proving can involve writing \ML{}

    64 code, possibly with Isabelle's sources at hand.  My book

    65 on~\ML{}~\cite{paulson91} covers much material connected with Isabelle,

    66 including a simple theorem prover.  Users must be familiar with logic as

    67 used in computer science; there are many good

    68 texts~\cite{galton90,reeves90}.

    69

    70 \index{LCF}

    71 {\sc lcf}, developed by Robin Milner and colleagues~\cite{gordon79}, is an

    72 ancestor of {\sc hol}, Nuprl, and several other systems.  Isabelle borrows

    73 ideas from {\sc lcf}: formulae are~\ML{} values; theorems belong to an

    74 abstract type; tactics and tacticals support backward proof.  But {\sc lcf}

    75 represents object-level rules by functions, while Isabelle represents them

    76 by terms.  You may find my other writings~\cite{paulson87,paulson-handbook}

    77 helpful in understanding the relationship between {\sc lcf} and Isabelle.

    78

    79 Isabelle does not keep a record of inference steps.  Each step is checked

    80 at run time to ensure that theorems can only be constructed by applying

    81 inference rules.  An Isabelle proof typically involves hundreds of

    82 primitive inferences, and would be unintelligible if displayed.

    83 Discarding proofs saves vast amounts of storage.  But can Isabelle be

    84 trusted?  If desired, object-logics can be formalized such that each

    85 theorem carries a proof term, which could be checked by another program.

    86 Proofs can also be traced.

    87

    88 \index{Isabelle!release history} Isabelle was first distributed in 1986.

    89 The 1987 version introduced a higher-order meta-logic with an improved

    90 treatment of quantifiers.  The 1988 version added limited polymorphism and

    91 support for natural deduction.  The 1989 version included a parser and

    92 pretty printer generator.  The 1992 version introduced type classes, to

    93 support many-sorted and higher-order logics.  The current version provides

    94 greater support for theories and is much faster.  Isabelle is still under

    95 development and will continue to change.

    96

    97 \subsubsection*{Overview}

    98 This manual consists of three parts.

    99 Part~I discusses the Isabelle's foundations.

   100 Part~II, presents simple on-line sessions, starting with forward proof.

   101 It also covers basic tactics and tacticals, and some commands for invoking

   102 Part~III contains further examples for users with a bit of experience.

   103 It explains how to derive rules define theories, and concludes with an

   104 extended example: a Prolog interpreter.

   105

   106 Isabelle's Reference Manual and Object-Logics manual contain more details.

   107 They assume familiarity with the concepts presented here.

   108

   109

   110 \subsubsection*{Acknowledgements}

   111 Tobias Nipkow contributed most of the section on Defining Theories''.

   112 Sara Kalvala and Markus Wenzel suggested improvements.

   113

   114 Tobias Nipkow has made immense contributions to Isabelle, including the

   115 parser generator, type classes, and the simplifier.  Carsten Clasohm, Sonia

   116 Mahjoub, Karin Nimmermann and Markus Wenzel also made improvements.

   117 Isabelle was developed using Dave Matthews's Standard~{\sc ml} compiler,

   118 Poly/{\sc ml}.  Many people have contributed to Isabelle's standard

   119 object-logics, including Martin Coen, Philippe de Groote, Philippe No\"el.

   120 The research has been funded by the SERC (grants GR/G53279, GR/H40570) and

   121 by ESPRIT (projects 3245: Logical Frameworks, and 6453: Types).

   122

   123 \newpage

   124 \pagestyle{plain} \tableofcontents

   125 \newpage

   126

   127 \newfont{\sanssi}{cmssi12}

   128 \vspace*{2.5cm}

   129 \begin{quote}

   130 \raggedleft

   131 {\sanssi

   132 You can only find truth with logic\\

   133 if you have already found truth without it.}\\

   134 \bigskip

   135

   136 G.K. Chesterton, {\em The Man who was Orthodox}

   137 \end{quote}

   138

   139 \clearfirst  \pagestyle{headings}

   140 \include{foundations}

   141 \include{getting}

   142 \include{advanced}

   143

   144

   145 \bibliographystyle{plain} \small\raggedright\frenchspacing

   146 \bibliography{atp,funprog,general,logicprog,theory}

   147

   148 \input{intro.ind}

   149 \end{document}